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June 28, 2005

Here a Pod, There a Pod

iTunes 4.9 is out, with its previously-announced support for podcasts. The podcast directory at the iTunes Music Store is very extensive, and makes subscribing to a podcast the same one-click experience that iTMS users are accustomed to for purchasing music.

Update:

Apple has published the specification for its iTunes extensions to the RSS 2.0 format used by podcasters. If you submit your podcast feed for inclusion in the iTMS podcast directory, you’re supposed to use these extensions to embed the podcast metadata, which will be displayed by the Music Store. [via Sam Ruby]

June 27, 2005

Topological G2 Sigma Models

de Boer, Naqvi and Shomer have a very interesting paper, in which they claim to construct a topological version of the supersymmetric σ\sigma-model on a 7-manifold of G2G_2 holonomy. The construction is quite a bit more delicate than the usual topologically-twisted σ\sigma-model. The latter are local 2D field theories, in which the spins of the fields have been shifted in such a way that one of the (nilpotent) supercharges becomes a scalar. If you wish, you can think of them as a 3-stage process:

Start with the original “untwisted” σ\sigma-model.

Twist, to form a local, but nonunitary field theory.

Pass to the QQ-cohomology, which finally yields a unitary theory (with, in fact, a finite-dimensional Hilbert space of states).

In their construction, the observables (and, for that matter, the nilpotent “scalar” supercharge itself) are nonlocal operators, defined as projections onto particular conformal blocks in the underlying CFT. So there is no intermediate “step 2”, at least not one that is recognizable as a local field theory.

June 19, 2005

Reconnection Probability

Much of the recent resurgence of interest in cosmic strings has to do with the possibility that such strings might be string-theoretic in nature, and that their properties might be observationally-distinguishable from those of “ordinary” field-theoretic cosmic strings.

June 17, 2005

Open WebKit

Amid all the kerfuffle about Apple moving to Intel processors, one important piece of news got underplayed. WebKit1, the system framework used by Safari (and other MacOSX applications), is now open-source. This is great news, as it means faster bug fixes and greater community involvement in the development of Apple’s flagship browser.

June 16, 2005

Ricci Flat

Matt Headrick and Toby Wiseman have finally come out with their paper on Ricci-flat metrics on K3. I’ve talked to them a fair bit about it; in fact, I take some personal satisfaction in having urged Matt to pursue this work.

The problem is as follows. Calabi conjectured (1954), and Yau proved (1976) the existence of a Ricci-flat metric for complex Kähler manifolds with trivial canonical class. But, when such manifolds are compact, they have no continuous isometries. So, though you know existence, actually finding such Ricci-flat metric — the solution to a complicated, nonlinear PDE — seemed impossibly hard.

Matt and Toby figured out how to do this numerically, at least for manifolds with a lot of discrete symmetries. It’s an incredible computational tour de force, as well as having some interesting physics applications.